The tapered roller bearing has higher load carrying capacity and higher rigidity than a ball bearing. Therefore, the tapered roller bearing is used in a vehicular pinion-shaft supporting assembly such as an automotive differential gear assembly or a transaxle assembly. However, the tapered roller bearing also suffers a drawback of having a great running torque (loss). In this connection, proposals have been made to reduce rolling friction by forming crownings on raceways of inner and outer rings or on rolling contact surfaces of tapered rollers (see, for example, Japanese Unexamined Patent Publications No.2003-130059 and No.2001-65574).
The above prior-art examples are designed to improve the performance of the tapered roller bearing by defining the configuration of the crowning on the raceway or on the rolling contact surface. However, the crowning has never been approached from the viewpoint of quantity. Hence, no attempt has been made to reduce the running torque of the tapered roller bearing by defining the quantity or the like of the crowning. On the other hand, rolling viscous resistance of the tapered rollers and oil agitation loss constitute major factors of the great running torque of the tapered roller bearing such as mounted in the differential gear assembly or the like. However, a guideline for reducing these resistances has not been defined.